Modeling the spread of disease requires 3 variables S, the # of ppl who can become sick, I, the number that are sick, and R, the number of ppl who have been sick but can't become again. The model is important because it reveals the number of ppl that should be vaccinated, the amount of ppl that will be infected, and the time frame. All of this is important to monitor disease and save lives. As there are more sick, there are more "interactions" btwn I and S, which is proportional to S and I. The change in S over time is equal to the negative rate that members of S become I, which equals SI time a negative constant a. The change in the number of people sick euquals the rate ppl get sick minus the rate they are removed, because as the number of sick is dependent on S and R. The constants represent how quickly the disease spreads or how quickly ppl are removed. They must be constant because these quantities vary depending on disease or population, but are the same for each disease.
Challenges
Because the variables represent ppl from the same original population, i don't see why 3 different variables are needed.
Reflections.
How are naturally immune people factored in?
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